Further direct extractions of the transversity functions

The transversity function can be extracted in a direct way using the Collins asymmetries measured in SIDIS and the corresponding asymmetries from 𝑒+𝑒− annihilation data, provided that SIDIS asymmetries for proton and deuteron (neutron) targets at the same kinematics are available. The first extractions performed in 2015 using COMPASS and Belle data provided fairly accurate determinations of the 𝑢-quark transversity function, but were characterised by large statistical uncertainties on the 𝑑-quark transversity functions due to the low statistics measurements with the deuteron data. The COMPASS Collaboration used the results from the data collected in 2022 with a transversely polarised deuteron target to extract the valence quarks transversity function, showing the impressive impact of the new data. Here we apply the same procedure to extract the sea quark transversity functions, which turn out to be again compatible with zero, despite the smaller statistical uncertainties. Also, we use the "difference asymmetries" to evaluate the ratio of the transversity functions of 𝑢 and 𝑑 valence quarks without using the Collins fragmentation functions. The ratio turns out to be about -0.5, almost constant over the investigated 𝑥-Bjorken range.